Highest Common Factor of 857, 2219 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 857, 2219 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 857, 2219 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 857, 2219 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 857, 2219 is 1.
HCF(857, 2219) = 1
HCF of 857, 2219 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 857, 2219 is 1.
Highest Common Factor of 857,2219 is 1
Step 1: Since 2219 > 857, we apply the division lemma to 2219 and 857, to get
2219 = 857 x 2 + 505
Step 2: Since the reminder 857 ≠ 0, we apply division lemma to 505 and 857, to get
857 = 505 x 1 + 352
Step 3: We consider the new divisor 505 and the new remainder 352, and apply the division lemma to get
505 = 352 x 1 + 153
We consider the new divisor 352 and the new remainder 153,and apply the division lemma to get
352 = 153 x 2 + 46
We consider the new divisor 153 and the new remainder 46,and apply the division lemma to get
153 = 46 x 3 + 15
We consider the new divisor 46 and the new remainder 15,and apply the division lemma to get
46 = 15 x 3 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 2219 is 1
Notice that 1 = HCF(15,1) = HCF(46,15) = HCF(153,46) = HCF(352,153) = HCF(505,352) = HCF(857,505) = HCF(2219,857) .
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Frequently Asked Questions on HCF of 857, 2219 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 857, 2219?
Answer: HCF of 857, 2219 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 857, 2219 using Euclid's Algorithm?
Answer: For arbitrary numbers 857, 2219 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.